This text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behavior, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behavior, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.

### Contents

Preface; 1. Phase transitions in simple systems; 2. Mean field theory; 3. The renormalization group idea; 4. Phase diagrams and fixed points; 5. The perturbative renormalization group; 6. Near two dimensions; 7. Surface critical behaviour; 8. Random systems; 9. Polymer statistics; 10. Critical dynamics; 11. Conformal symmetry; Appendix: Gaussian integration; Selected bibliography; Index.

### Reviews

"Cardy has made significant contributions to almost all the topics covered in the second half of the book, and he has been one of the leaders in developing the use of conformal invariance in statistical mechanics....I think this challenging book will prove evry useful to those trying to learn the subject, provided that they take the time to read widely in the supplementary references." David Thouless, Physics Today

"The book may be advised for physics graduate students and for professionals who want to get an introduction to one of the most creative concepts of modern physics." Sergei A. Nemnyugin, Mathematical Reviews